Inverse Nodal Problem for the Sturm-Liouville Operator with Three Discontinuities (Journal of Computational Mathematics, 2025)
In this work, the inverse nodal problem for the Sturm-Liouville operator with three discontinuities is studied. It is proved that the dense nodes of the eigenfunctions can uniquely determine the potential on the whole interval and some parameters, and a reconstruction algorithm for the solution is presented. Finally, numerical examples were provided, and the effectiveness of the algorithm was verified through numerical calculations.
Keywords: Inverse nodal problems; Discontinuities; Uniqueness theorem; Reconstruction algorithm